Thanks for asking ask a doctor service from doctor spring. I understand your problem and will try to answer your queries the best possible. There is no reason to freak out. The dry skin u described over the shaft on the penis probably is due to irritant contact dermatitis following repeated exposure to lubricants like harsh soaps resulting in an allergic reaction. It is also known as a penis rash and usually presents with dry, flaky skin, inflammation and associated with itching.
However other causes of dry skin like infection such as candida, psoriasis cannot be completely excluded. It could also be due to friction caused by rubbing of your clothing.
I would recommend a few methods you could try to reduce the dryness:
a) Use a mild soap while cleansing yourself.
b) Use a lubricant while masturbating.
c) You can use loose fabrics to prevent friction.
d) Apply coconut oil over the dry area.
You can use anti histaminic drug like cetirizine at bedtime for 2 days .if it still doesn't subside you can consult your dermatologist. Hope this helps. If there s any further queries do let me know.